DERIVATIVE OF NATURAL LOG OF SQUARE ROOT OF X

We know the derivative of lnx, which is ¹⁄ₓ.

(lnx)' = ¹⁄ₓ

We can find the derivative of ln(√x) using one of the following two methods.

Method 1 (Using Chain Rule) :

If y = ln(√x), find ᵈʸ⁄dₓ.

Let t = √x.

Then, we have

y = lnt

By chain rule,

Substitute y = lnt and t = √x.

Substitute t = √x.

Therefore,

Method 2 (Without Chain Rule) :

If y = ln(√x), find ᵈʸ⁄dₓ.

Use the Power Rule of Logarithms.

Find the derivative on both sides with respect to x.

Therefore,

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